Question

Find the value of: ${\log }_{3}4.{\log }_{4}5.{\log }_{5}6.{\log }_{5}7.{\log }_{7}8.{\log }_{7}8.{\log }_{8}9.$

Answer 1

${\log }_{3}4.{\log }_{4}5.{\log }_{5}6.{\log }_{5}7.{\log }_{7}B.{\log }_{7}B.{\log }_{8}9$

$\Rightarrow \frac{\log 4}{\log 3}\times \frac{\log 5}{\log 4}\times \frac{\log 7}{\log 6}\times \frac{\log 7}{\log 6}\times \frac{\log 8}{\log 7}\times \frac{\log 9}{\log 8}=\frac{\log 9}{\log 3}=2.$